The application of Bayesian probabilistic reasoning in general (as described in this video) is not the same thing as "Bayesian statistics" specifically, which usually to modeling and posterior inference using both a likelihood model and a prior model. It's a very different approach to statistical inference both in theory and in practice. This creator himself is either ignorant of this distinction or is trying to mislead his viewers in order to dunk on the FDA. It's obvious from the video comments that many people have indeed been misled as to what Bayesian statistics is and what the implications of its might be in the context of clinical trials.

Indeed, even more broadly online "Bayesian" seems to have taken on the form of "I know Bayes' Rule and think about base rates" as opposed to "Do you prefer jags or stan for MCMC?"